Fresnel lenses are typically round when viewed from their front and as such, their form factor may not be usable in some situations. For example, where a small and/or polygonal implementation is needed, such round devices may not fit within the area in which the lens is needed.
Further, in some implementations, a wide field of view may be desired. However, a Fresnel lens has a limited field of view that may be too limited to be usable in such implementations.
In some implementations, an array of Fresnel lenses can be used to create discrete detection zones and increase the field of view. A flat Fresnel lens array will generate low optical efficiency in the outer elements of the array due to off-axis issues. A cylindrical or spherical formation can be used to somewhat mitigate the off-axis efficiency issues.
However, although a cylindrical or spherical lens array would be optically more efficient, a flat lens array may be required for cosmetic reasons or due to the area available within the form factor of the device on which the lens array is to be mounted. In a cylindrical or spherical array, each element in the array can be oriented such that the normal vector to the center of the lens (e.g., optical axis of each lens element) points toward a detection zone that the lens element is intended to detect motion in.
In this on-axis lens orientation, an image focused on a pyroelectric sensor's detector of a target (e.g., from a human) in that lens element's detection zone will form a nicely focused and un-abberated image. Additionally, all lens elements in a cylindrical or spherical lens array can be of a single focal length equal to the radius of curvature of the array. In a traditional flat Fresnel lens array, a lens element in the center of the array directly in front of the pyroelectric sensor will generate an image of a target on the detectors that is in focus and un-abberated when the correct focal length Fresnel lens is used. However, as the target moves off center and lens elements are placed to the side of lens center, the images generated using lens elements of the same focal length become more and more out of focus.
To compensate, longer focal lengths are used as elements depart from center. The off axis effects produce more and more abberated images as elements depart from center even when using the appropriate focal lengths resulting in progressively less energy reaching the pyro detectors as more energy goes above, below, to the left, and to the right of the pyroelectric sensors detectors.
In an attempt to compensate for the out of focus issue, the lens designer can progressively increase the element focal lengths to balance the energy on each detector and increase the element size progressively as the elements depart from the center position. The goal of increasing the element size is to achieve the same amount of energy landing on the pyro detector when the target is in one of the two detection zones of a side lens element as when the target is in one of the two detection zones of the center lens element.
There is a limit to the lens size of these side elements in a flat lens array wherein increasing the size of the element beyond a certain size no longer results in a proportional increase in energy and ultimately results in no increase in energy landing on the detectors of the pyroelectric (pyro) sensors. It is this issue that limits the practical horizontal field of view angle of a flat Fresnel lens array. This can be an issue, for example, where it is desirable to have near the same level of energy landing on the pyro detectors from a target at 9.5 meters distance in detection zones coming from the outside lens elements reaching horizontally as far as 60° off axis, as that landing on the pyro detectors from a target at 12.0 meters distance, in detection zones coming from the center lens element, where the image is on-axis.